Simple features and the R spatial zoo
Michael Sumner
2016-11-09
Base graphics
p1 <- cbind(x = c(0, 0, 0.75, 1, 0.5, 0.8, 0.69, 0),
y = c(0, 1, 1, 0.8, 0.7, 0.6, 0, 0))
p2 <- cbind(x = c(0.2, 0.2, 0.3, 0.5, 0.5, 0.2),
y = c(0.2, 0.4, 0.6, 0.4, 0.2, 0.2))
p4 <- cbind(x = c(0.69, 0.8, 1.1, 1.23, 0.69),
y = c(0, 0.6, 0.63, 0.3, 0))
pp <- rbind(p1, NA, p2[nrow(p2):1, ])
plot(rbind(pp, p4), cex = 1.3, main = "two polygons, shared edge")
polypath(pp, col = "grey")
polypath(p4, col = "firebrick")
Simple features for R
#devtools::install_github("edzer/sfr")
library(sf)
library(tibble)
x <- st_as_sf(tibble(a = 1:2, geom = st_sfc(list(st_multipolygon(list(list(p1, p2[rev(seq(nrow(p2))), ]))),
st_multipolygon(list(list(p4)))))))
plot(x, col = c("grey", "firebrick"))
Spatial (legacy sp package)
library(sp)
spgdf <- as(x, "Spatial")
plot(spgdf, col = c("grey", "firebrick"))
Grammar of graphics
## fortify model
library(dplyr)
meta <- as_tibble(x %>% dplyr::select(-geom) %>% mutate(object_ = row_number()))
map <- spbabel::sptable(spgdf)
library(ggplot2)
ggcols <- ggplot2::scale_fill_manual(values = c("1" = "grey", "2" = "firebrick"))
ggplot(map %>% mutate(rn = row_number()) %>% inner_join(meta)) + aes(x = x_, y = y_, group = branch_, fill = factor(object_)) +
ggcols + ggpolypath::geom_polypath() + geom_path()## Joining, by = "object_"
Map table
library(spbabel)
mp <- map_table(spgdf)
ggcols <- ggplot2::scale_fill_manual(values = setNames(c("grey", "firebrick"), mp$o$object_))
gg <- ggplot(mp$o %>% inner_join(mp$b) %>% inner_join(mp$bXv) %>% inner_join(mp$v))## Joining, by = "object_"## Joining, by = "branch_"## Joining, by = "vertex_"gg + aes(x = x_, y = y_, group = branch_, fill = object_) + ggcols + ggpolypath::geom_polypath() + geom_path(lwd = 2)
Planar straight line graph
## purrring function
p2seg <- function(x) as_tibble(rangl:::path2seg(x$vertex_))
BxE <- mp$bXv %>% split(.$branch_) %>% purrr::map(p2seg) %>% bind_rows(.id = "branch_")
ggplot(BxE %>% inner_join(mp$v %>% rename(x = x_, y = y_), c("V1" = "vertex_")) %>%
inner_join(mp$v, c("V2" = "vertex_"))) +
geom_segment(aes(x = x, y = y, xend = x_, yend = y_, colour = V1)) + guides(colour = FALSE)
Arc-node
These are the nodes in the graph, we need to traverse the edges to determine the arc-branches, and anything left is just a standalone arc. This is brute-force remove duplicate edges (ignore direction), join on start vertex, end vertex, count the number of edges involved and any with 3 edges is a Node.
## what are the nodes?
x1 <- st_read(system.file("shape/nc.shp", package="sf"), "nc", crs = 4267)## Reading layer `nc' from data source `C:/inst/R/R/library/sf/shape/nc.shp' using driver `ESRI Shapefile'
## features: 100
## fields: 14
## converted into: MULTIPOLYGON
## proj4string: +proj=longlat +datum=NAD27 +no_defsmp <- spbabel::map_table(x1)
uE <- mp$bXv %>% split(.$branch_) %>% purrr::map(p2seg) %>% bind_rows(.id = "branch_")%>% mutate(edge_ = row_number()) %>%
mutate(uu = paste(pmin(V1, V2), pmax(V1, V2), sep = "_")) %>% distinct(uu, .keep_all = TRUE)
nodes <- bind_rows(mp$v %>% dplyr::select(vertex_) %>% inner_join(uE, c("vertex_" = "V1")),
mp$v %>% dplyr::select(vertex_) %>% inner_join(uE, c("vertex_" = "V2"))) %>%
distinct(edge_, vertex_) %>%
group_by(vertex_) %>% mutate(nb = n()) %>% ungroup() %>%
filter(nb > 2) %>% distinct(vertex_) %>% inner_join(mp$v)## Joining, by = "vertex_"plot(x1)
points(nodes$x_, nodes$y_, cex = 0.9)
Simplicial complex
sc <- rangl::rangl(spgdf)
plot(x)
l1 <- inner_join(sc$o[1, ], sc$t) %>% split(.$triangle_) %>% purrr::map(function(x) inner_join(x, sc$tXv) %>% inner_join(sc$v)) ## Joining, by = "object_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"j <- lapply(l1, function(x) polygon(cbind(x$x_, x$y_), col = "grey"))
l2 <- inner_join(sc$o[2, ], sc$t) %>% split(.$triangle_) %>% purrr::map(function(x) inner_join(x, sc$tXv) %>% inner_join(sc$v)) ## Joining, by = "object_"## Joining, by = "triangle_"## Joining, by = "vertex_"## Joining, by = "triangle_"## Joining, by = "vertex_"j <- lapply(l2, function(x) polygon(cbind(x$x_, x$y_), col = "firebrick"))
set.seed(75)
sc <- rangl::rangl(as(x1, "Spatial"))
plot(x1)
for (i in seq(nrow(x1))) {
l1 <- inner_join(sc$o[i, ], sc$t, "object_") %>% split(.$triangle_) %>% purrr::map(function(x) inner_join(x, sc$tXv, "triangle_") %>% inner_join(sc$v, "vertex_"))
j <- lapply(l1, function(x) polygon(cbind(x$x_, x$y_), border = sample(c("grey", "firebrick", viridis::viridis(5)), 1)))
}
Spatial normal forms
In this document I describe a “normal-form” that provides a very general way of extending the traditional GIS forms, and is a bridge between vector and raster rather than being a different form altogether. The purpose of this document is to advocate for this general form of data organization that can be used for new extended uses of GIS. I’m not arguing that this be used in place of other optimized forms, although it can be: I am interested in operations that simply cannot be performed already.
When we talk about vector data in geo-spatial, we have at least three levels of hierarchy to consider in the data structures.
- objects (or features) - these are the things we primarily interact with and store data against
- coordinates - these are the specific vertices, the dimensionless points that place our data in a geometry
- branches - these are the parts that different objects are made of, they describe the way the coordinates are linked together, the topology
GIS tools typically only provides direct access to the objects, though the relations between branches and coordinates can sometimes be seen.
We generally cannot store information against the branches or the coordinates, beyond what they inherently are defined by. For coordinates this is the X and Y values, and/or the longitude and latitudes, but simple features does provide the ability to store a “third” coordinate “Z” and or a measure coordinate “M”. M is typically used for “linear referencing”, and not a more general multidimensional geometry (like time).
I’ll use the countries example from a GeoPackage file provided here. I use R because I can tell the complete story with it, in a concrete and reproducible way.
Read in a polygon vector layer in traditional GIS form, and plot it.
#library(rworldmap)
#data(countriesLow)
#p <- countriesLow
library(rgdal)
p <- readOGR(system.file("extdata", "small_world.gpkg", package = "rangl"), "ne_110m_admin_0_countries")## OGR data source with driver: GPKG
## Source: "C:/inst/R/R/library/rangl/extdata/small_world.gpkg", layer: "ne_110m_admin_0_countries"
## with 177 features
## It has 1 fieldsplot(p, col = viridis::viridis(nrow(p)))
This object p presents a “data frame” (i.e. a table) front-end that we can query and use at the objects level, much like in some GIS software we can easily select a single object or row in a table.
library(spbabel)
(pnganz <- subset(p, name %in% c("Australia", "Indonesia", "New Zealand", "Papua New Guinea")))## class : SpatialPolygonsDataFrame
## features : 4
## extent : 95.29303, 178.5171, -46.64124, 5.479821 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
## variables : 1
## # A tibble: 4 × 1
## name
## * <fctr>
## 1 Australia
## 2 Indonesia
## 3 New Zealand
## 4 Papua New Guineapnganz$color <- viridis::viridis(nrow(pnganz))
plot(pnganz, col = viridis::viridis(nrow(pnganz)))
Looking at the object’s underlying geometric structure shows nested lists of matrixes of x,y coordinates. There is one matrix per branch, analogous to the way that feature parts are nested in standard Geom binary forms like WKB. Each component branch stores extra information about whether it is a hole, the ring direction, a coordinate for label plotting and so on. We otherwise cannot store any more information on the component parts though.
str(geometry(pnganz[1, ]))## Formal class 'SpatialPolygons' [package "sp"] with 4 slots
## ..@ polygons :List of 1
## .. ..$ :Formal class 'Polygons' [package "sp"] with 5 slots
## .. .. .. ..@ Polygons :List of 2
## .. .. .. .. ..$ :Formal class 'Polygon' [package "sp"] with 5 slots
## .. .. .. .. .. .. ..@ labpt : num [1:2] 147 -42
## .. .. .. .. .. .. ..@ area : num 7.18
## .. .. .. .. .. .. ..@ hole : logi FALSE
## .. .. .. .. .. .. ..@ ringDir: int 1
## .. .. .. .. .. .. ..@ coords : num [1:17, 1:2] 145 146 147 148 148 ...
## .. .. .. .. ..$ :Formal class 'Polygon' [package "sp"] with 5 slots
## .. .. .. .. .. .. ..@ labpt : num [1:2] 134.4 -25.6
## .. .. .. .. .. .. ..@ area : num 688
## .. .. .. .. .. .. ..@ hole : logi FALSE
## .. .. .. .. .. .. ..@ ringDir: int 1
## .. .. .. .. .. .. ..@ coords : num [1:224, 1:2] 144 144 145 145 145 ...
## .. .. .. ..@ plotOrder: int [1:2] 2 1
## .. .. .. ..@ labpt : num [1:2] 134.4 -25.6
## .. .. .. ..@ ID : chr "9"
## .. .. .. ..@ area : num 696
## ..@ plotOrder : int 1
## ..@ bbox : num [1:2, 1:2] 113.3 -43.6 153.6 -10.7
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:2] "x" "y"
## .. .. ..$ : chr [1:2] "min" "max"
## ..@ proj4string:Formal class 'CRS' [package "sp"] with 1 slot
## .. .. ..@ projargs: chr "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"NOTE: the Spatial classes here are pre-simple features, so they are more analogous to the structures in a shapefile in that a polygon hole’s “island parent”" may be ambiguous, but this is not so important to this story. R now has simple features in the sfr project here, which adds Z, M and the possibility of some of the exotic types as well. https://github.com/edzer/sfr
These hierarchical structures can be serialized and stored in different ways, typically they are stored as binary geoms and stored directly in a table. As the Spatial Data topic says under “Why Geoms and not More Normal Form?” this is very performant, since a small number of large records can be optimized better compared to a large number of small records.
An interesting aspect here is that these structures don’t describe the topology of the objects in any special way, these are just paths of coordinates, and when they are plotted or used in analysis there’s a rule about how space is enclosed by a closed path. If we treat them as lines, the only difference is to not treat them as enclosed paths. Literally the only difference in the structure of this object from the polygons version is the name of the class, and the behaviour that methods invoked for this object will provide.
plot(as(pnganz, "SpatialLinesDataFrame"))
plot(as(pnganz, "SpatialLinesDataFrame"), col = viridis::viridis(nrow(pnganz), alpha = 0.7), lwd = c(2, 4), add = TRUE)
str(as(geometry(pnganz[1,]), "SpatialLines"))## Formal class 'SpatialLines' [package "sp"] with 3 slots
## ..@ lines :List of 1
## .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
## .. .. .. ..@ Lines:List of 2
## .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
## .. .. .. .. .. .. ..@ coords: num [1:17, 1:2] 145 146 147 148 148 ...
## .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
## .. .. .. .. .. .. ..@ coords: num [1:224, 1:2] 144 144 145 145 145 ...
## .. .. .. ..@ ID : chr "9"
## ..@ bbox : num [1:2, 1:2] 113.3 -43.6 153.6 -10.7
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:2] "x" "y"
## .. .. ..$ : chr [1:2] "min" "max"
## ..@ proj4string:Formal class 'CRS' [package "sp"] with 1 slot
## .. .. ..@ projargs: chr "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"If we convert these data to “normal form”, we actually need at least three tables, one each for the objects, the branches, and the coordinates (vertices). The map_table function in the spbabel package creates these but also adds another link table between branches and vertices to enable de-duplication of shared vertices. The de-duplication is required for triangulating the polygons, and other topological operations.
ptabs <- spbabel::map_table(pnganz)
print(names(ptabs))## [1] "o" "b" "bXv" "v"print(sapply(ptabs, nrow))## o b bXv v
## 4 21 638 614Now it’s a bit clearer how the underlying entities are put together. Each table here has a unique relational id, this allows us to subset and recombine these tables without having to convert indexes each time.
The objects.
ptabs$o## # A tibble: 4 × 3
## name color object_
## * <fctr> <chr> <chr>
## 1 Australia #440154FF Xi6lLME7sH
## 2 Indonesia #31688EFF An1jFbGb4n
## 3 New Zealand #35B779FF GUnpistmM9
## 4 Papua New Guinea #FDE725FF YrfpYFDjrLThe branches record which object they belong to.
ptabs$b## # A tibble: 21 × 3
## object_ branch_ island_
## <chr> <chr> <lgl>
## 1 Xi6lLME7sH JZVK8n1144 TRUE
## 2 Xi6lLME7sH kpPlSEp2ZO TRUE
## 3 An1jFbGb4n DxGJxvAnuv TRUE
## 4 An1jFbGb4n r93HaVhN6a TRUE
## 5 An1jFbGb4n R4jejRslp5 TRUE
## 6 An1jFbGb4n yBxdFBUc77 TRUE
## 7 An1jFbGb4n 0SVR7GeWYJ TRUE
## 8 An1jFbGb4n 4rAfhuEqlF TRUE
## 9 An1jFbGb4n DYjtFAEVNt TRUE
## 10 An1jFbGb4n QTJa5kvRVT TRUE
## # ... with 11 more rowsThe branches-link-vertex table records the relationship between vertices and branches (by default the de-duplication is done in X-Y but it could be done in other geometric spaces, e.g. in 1D time or 3D X-Y-Z or X-Y-Time).
This is the instances of vertices as opposed to the unique paired values of coordinates themselves.
ptabs$bXv## # A tibble: 638 × 3
## branch_ order_ vertex_
## <chr> <int> <chr>
## 1 JZVK8n1144 1 cWqEryQCkm
## 2 JZVK8n1144 2 Tu7QtgiNtJ
## 3 JZVK8n1144 3 Ydn952ztO7
## 4 JZVK8n1144 4 3wKgLyOLtS
## 5 JZVK8n1144 5 XowmjXFTNs
## 6 JZVK8n1144 6 lH6N3bX6BT
## 7 JZVK8n1144 7 rV61ZojjmF
## 8 JZVK8n1144 8 3vADss9R04
## 9 JZVK8n1144 9 aiHOq96aGT
## 10 JZVK8n1144 10 jYOVK6n9c4
## # ... with 628 more rowsAnd finally the vertices. In this example there are fewer unique x-y vertex than there are instance of the vertices, not a one-to-one match. This discrepancy obviously increases greatly for layers with shared boundaries, though in this example it is mostly due to the final closing coordinate on each polygon path - it’s a repeated instance, but not a repeated vertex value. There is at least one shared edge in this layer, clearly the one between Indonesia and Papua New Guinea.
ptabs$v## # A tibble: 614 × 3
## x_ y_ vertex_
## <dbl> <dbl> <chr>
## 1 145.3980 -40.79255 cWqEryQCkm
## 2 146.3641 -41.13770 Tu7QtgiNtJ
## 3 146.9086 -41.00055 Ydn952ztO7
## 4 147.6893 -40.80826 3wKgLyOLtS
## 5 148.2891 -40.87544 XowmjXFTNs
## 6 148.3599 -42.06245 lH6N3bX6BT
## 7 148.0173 -42.40702 rV61ZojjmF
## 8 147.9141 -43.21152 3vADss9R04
## 9 147.5646 -42.93769 aiHOq96aGT
## 10 146.8703 -43.63460 jYOVK6n9c4
## # ... with 604 more rowsPolygons are just lines
From this form we can see clearly that polygons and lines in GIS are really the same thing, we have paths of coordinates and then rules about how they are used.
If we compare each entity table side by side it’s clear the only difference is whether a branch is badged as an island vs. a hole.
For points we don’t need the branches or the order data, though for multipoints we do need branch.
ltabs <- spbabel::map_table(as(pnganz, "SpatialLinesDataFrame"))
for (i in seq_along(ltabs)) {
writeLines("------------------------------")
print(ltabs[i])
print(ptabs[i])
writeLines("")
}## ------------------------------
## $o
## # A tibble: 4 × 3
## name color object_
## * <fctr> <chr> <chr>
## 1 Australia #440154FF Zjv26GQ4MD
## 2 Indonesia #31688EFF LYBjIjKgl2
## 3 New Zealand #35B779FF Smb3tFYdCv
## 4 Papua New Guinea #FDE725FF yPSQLfCyr3
##
## $o
## # A tibble: 4 × 3
## name color object_
## * <fctr> <chr> <chr>
## 1 Australia #440154FF Xi6lLME7sH
## 2 Indonesia #31688EFF An1jFbGb4n
## 3 New Zealand #35B779FF GUnpistmM9
## 4 Papua New Guinea #FDE725FF YrfpYFDjrL
##
##
## ------------------------------
## $b
## # A tibble: 21 × 2
## object_ branch_
## <chr> <chr>
## 1 Zjv26GQ4MD 3FzAJk9QRs
## 2 Zjv26GQ4MD I9P4DFq3b2
## 3 LYBjIjKgl2 dAmkg86XWt
## 4 LYBjIjKgl2 c0PTsbpMky
## 5 LYBjIjKgl2 GHQzGxsZ4f
## 6 LYBjIjKgl2 5PqWlF31mn
## 7 LYBjIjKgl2 bfObQ03ghA
## 8 LYBjIjKgl2 lpHixist48
## 9 LYBjIjKgl2 UPGrjtEo9T
## 10 LYBjIjKgl2 QPK4MOKyWk
## # ... with 11 more rows
##
## $b
## # A tibble: 21 × 3
## object_ branch_ island_
## <chr> <chr> <lgl>
## 1 Xi6lLME7sH JZVK8n1144 TRUE
## 2 Xi6lLME7sH kpPlSEp2ZO TRUE
## 3 An1jFbGb4n DxGJxvAnuv TRUE
## 4 An1jFbGb4n r93HaVhN6a TRUE
## 5 An1jFbGb4n R4jejRslp5 TRUE
## 6 An1jFbGb4n yBxdFBUc77 TRUE
## 7 An1jFbGb4n 0SVR7GeWYJ TRUE
## 8 An1jFbGb4n 4rAfhuEqlF TRUE
## 9 An1jFbGb4n DYjtFAEVNt TRUE
## 10 An1jFbGb4n QTJa5kvRVT TRUE
## # ... with 11 more rows
##
##
## ------------------------------
## $bXv
## # A tibble: 638 × 3
## branch_ order_ vertex_
## <chr> <int> <chr>
## 1 3FzAJk9QRs 1 9lwJVGsu7j
## 2 3FzAJk9QRs 2 x4ZurkkDEa
## 3 3FzAJk9QRs 3 gWMDJMgBwQ
## 4 3FzAJk9QRs 4 zDB14GipkU
## 5 3FzAJk9QRs 5 hmkkXNHlmv
## 6 3FzAJk9QRs 6 FuX8RhryqB
## 7 3FzAJk9QRs 7 cPKqPbSHzv
## 8 3FzAJk9QRs 8 pKq4h283zW
## 9 3FzAJk9QRs 9 vtZbDDAiqp
## 10 3FzAJk9QRs 10 NGb48CN0W6
## # ... with 628 more rows
##
## $bXv
## # A tibble: 638 × 3
## branch_ order_ vertex_
## <chr> <int> <chr>
## 1 JZVK8n1144 1 cWqEryQCkm
## 2 JZVK8n1144 2 Tu7QtgiNtJ
## 3 JZVK8n1144 3 Ydn952ztO7
## 4 JZVK8n1144 4 3wKgLyOLtS
## 5 JZVK8n1144 5 XowmjXFTNs
## 6 JZVK8n1144 6 lH6N3bX6BT
## 7 JZVK8n1144 7 rV61ZojjmF
## 8 JZVK8n1144 8 3vADss9R04
## 9 JZVK8n1144 9 aiHOq96aGT
## 10 JZVK8n1144 10 jYOVK6n9c4
## # ... with 628 more rows
##
##
## ------------------------------
## $v
## # A tibble: 614 × 3
## x_ y_ vertex_
## <dbl> <dbl> <chr>
## 1 145.3980 -40.79255 9lwJVGsu7j
## 2 146.3641 -41.13770 x4ZurkkDEa
## 3 146.9086 -41.00055 gWMDJMgBwQ
## 4 147.6893 -40.80826 zDB14GipkU
## 5 148.2891 -40.87544 hmkkXNHlmv
## 6 148.3599 -42.06245 FuX8RhryqB
## 7 148.0173 -42.40702 cPKqPbSHzv
## 8 147.9141 -43.21152 pKq4h283zW
## 9 147.5646 -42.93769 vtZbDDAiqp
## 10 146.8703 -43.63460 NGb48CN0W6
## # ... with 604 more rows
##
## $v
## # A tibble: 614 × 3
## x_ y_ vertex_
## <dbl> <dbl> <chr>
## 1 145.3980 -40.79255 cWqEryQCkm
## 2 146.3641 -41.13770 Tu7QtgiNtJ
## 3 146.9086 -41.00055 Ydn952ztO7
## 4 147.6893 -40.80826 3wKgLyOLtS
## 5 148.2891 -40.87544 XowmjXFTNs
## 6 148.3599 -42.06245 lH6N3bX6BT
## 7 148.0173 -42.40702 rV61ZojjmF
## 8 147.9141 -43.21152 3vADss9R04
## 9 147.5646 -42.93769 aiHOq96aGT
## 10 146.8703 -43.63460 jYOVK6n9c4
## # ... with 604 more rowsWhat makes polygons different to lines?
The coordinate-path structures used above for polygons and lines are very explicit, and in traditional form cannot be used in a more abstract way. By collecting the attributes of the entities in use into their own tables we start to build this abstraction. The paths are represented as a sequence of identifiers, rather than the actual coordinate values themselves. Why do this? We can abstract the choice of what do with those coordinate away from their storage. We also get a limited form of topology, in that a change made to one vertex coordinate attribute is reflected in all of the branches that use that vertex, analogous the Shared Edit mode in Manifold 8.0.
The next step in topological relationships is to represent each segment of a line rather than the entire path. To do this we need a table of segments, and a link table to store the identity of the two vertices used by those segments.
This has been implemented in the package rangl.
lsegment <- rangl::rangl(as(pnganz, "SpatialLinesDataFrame"))## Joining, by = "segment_"
## Joining, by = "segment_"as.data.frame(lapply(lsegment, nrow))## o v l lXv meta
## 1 4 614 617 1120 1This is no different for polygons when we store them as polygon paths, so then why is the segment/edge model useful? It provides a table to store metrics such as the length of the segment, its duration in time, and other information. The segment/edge model is also a required precursor for building a triangulated mesh. This brings us to an important stage of the story.
Polygons are not composed of primitives
Lines and polygons are stored as paths of coordinates, but lines can be decomposed to a more abstract form. Once in this form we can (in R) plot the lines much more quickly as segments, each with their own individual properties.
par(mar = rep(0, 4))
plot(lsegment$v$x_, lsegment$v$y_, asp = 1, pch = ".", axes = FALSE)
lines(lsegment$v$x_, lsegment$v$y_, col = viridis::viridis(4))
Not surprisingly, our connected line doesn’t make much sense, but worse our attempts at applying multiple colours was completely unsuccessful. Segments to the rescue.
par(mar = rep(0, 4))
plot(lsegment$v$x_, lsegment$v$y_, asp = 1, pch = ".", axes = FALSE)
lsegment$o$color <- viridis::viridis(nrow(lsegment$o))
segs <- lsegment$l %>% inner_join(lsegment$o %>% select(object_, color)) %>% inner_join(lsegment$lXv) %>% select(color, vertex_) %>% inner_join(lsegment$v)## Joining, by = "object_"## Joining, by = "segment_"## Joining, by = "vertex_"ix <- seq(1, nrow(segs), by = 2); segments(segs$x_[ix], segs$y_[ix], segs$x_[ix + 1], segs$y_[ix+1], col = segs$color[ix], lwd = 4)
This is not lovely code, though it is straight forward and systematic. Treated as segments we automatically get the right “topology” of our lines, we joined the object attribute down to the actual pairs of coordinates and plotted all the segments individually. We managed to keep our object-part-coordinate hierarchy, though we’ve chosen primitives belonging to objects rather than branches as the model. This is also convenient for the next step because line segments are what we need for generating primitives to represent the polygons as surfaces.
Constrained polygon triangulation starts with line primitives
Treat the polygon as segments build a triangulation, a surface of 2D triangle primitives.
prim2D <- rangl::rangl(pnganz)
plot(pnganz, border = "black", col = "transparent", lwd = 4)
for (i in seq(nrow(prim2D$t))) {
tri <- prim2D$t[i, ] %>% inner_join(prim2D$tXv, "triangle_") %>% inner_join(prim2D$v, "vertex_") %>% select(x_, y_)
polygon(tri$x_, tri$y_, border = (prim2D$t[i, ] %>% inner_join(prim2D$o, "object_"))$color[1])
}
The plot loop above is very inefficient, but it’s purely to illustrate that we have the shapes in the right form. This is used in rangl to plot the shapes in 3D, either in native planar form or as a surface of a globe.
library(rgl)
plot(prim2D, specular = "black")## Joining, by = "object_"## Joining, by = "triangle_"subid <- currentSubscene3d()
rglwidget(elementId="pnganz")## Joining, by = "object_"
## Joining, by = "triangle_"subid <- currentSubscene3d()
rglwidget(elementId="png_anz_globe")